J.C. Brem

Plane stress yield function for aluminum alloy sheets—part 1: theory

Abstract A new plane stress yield function that well describes the anisotropic behavior of sheet metals, in particular, aluminum alloy sheets, was proposed. The anisotropy of the function was introduced in the formulation using two linear transformations on the Cauchy stress tensor. It was shown that the accuracy of this new function was similar to that of other recently proposed non-quadratic yield functions. Moreover, it was proved that the function is convex in stress space. A new experiment was proposed to obtain one of the anisotropy coefficients. This new formulation is expected to be particularly suitable for finite element (FE) modeling simulations of sheet forming processes for aluminum alloy sheets.

A six-component yield function for anisotropic materials

Abstract In classical flow theory of plasticity, it is assumed that the yield surface of a material is a plastic potential. That is, the strain rate direction is normal to the yield surface at the corresponding loading state. Consequently, when the yield surface is known, it is possible to predict its flow behavior and, associated with some failure criteria, to predict limit strains above which failure occurs. In this work a new six-component yield surface description for orthotropic materials is developed. This new yield function has the advantage of being relatively simple mathematically and yet is consistent with yield surfaces computed with polycrystal plasticity models. The proposed yield function is independent of hydrostatic pressure. So, except for such cases, strain rates can be calculated for any loading condition. Applications of this new criterion for aluminum alloy sheets are presented. The uniaxial plastic properties determined for 2008-T4 and 2024-T3 sgeet samplesare compared to those predicted with the proposed constitutive model. In addition, for 2008-T4, the predictions of the six-component yield function are compared to those made with the plane stress tricomponent yield criterion proposed by Barlat and Lian. Though rather good agreement between experiments and predicted results is obtained, some discrepancies are observed. Better agreement could result if the isotropic work-hardening assumption associated with the yield criterion were relaxed. Nevertheless, the proposed yield function leads to plastic properties similar to those computed with polycrystalline plasticity models and can be very useful for describing the behavior of anisotropic materials in numerical simulation of forming processes

Yield function development for aluminum alloy sheets

In this work, yield surfaces were measured for binary aluminum-magnesium sheet samples which were fabricated by different processing paths to obtain different microstructures. The yielding behavior was measured using biaxial compression tests on cubic specimens made from laminated sheet samples. The yield surfaces were also predicted from a polycrystal model using crystallographic texture data as input and from a phenomenological yield function usually suitable for polycrystalline materials. The experimental yield surfaces were found to be in good agreement with the polycrystal predictions for all materials and with the phenomenological predictions for most materials. However, for samples processed with high cold rolling reduction prior to solution heat treatment, a significant difference was observed between the phenomenological and the experimental yield surfaces in the pure shear region. In this paper, a generalized phenomenological yield description is proposed to account for the behavior of the solute strengthened aluminum alloy sheets studied in this work. It is subsequently shown that this yield function is suitable for the description of the plastic behavior of any aluminum alloy sheet.

Yielding description for solution strengthened aluminum alloys

In this work, yield surfaces were measured for binary aluminum-magnesium sheet samples which were fabricated by different processing paths to obtain different microstructures. The yielding behavior was measured using biaxial compression tests on cubic specimens made from laminated sheet samples. The yield surfaces were also predicted from a polycrystal model using crystallographic texture data as input and from a phenomenological yield function proposed previously. In general, experimental and predicted yield surfaces were found to be in relatively good agreement. However, for samples processed with high cold rolling reduction prior to solution heat treatment, a significant difference was observed between the phenomenological yield surface and the experimental/polycrystal yield surfaces in the pure shear region. In this paper, a refinement was proposed for the phenomenological yield description to account for the behavior of the solute strengthened aluminum alloy sheets studied in this work, and in general, for any sheet metal. This yield function was implemented into a finite element code and sample computations were carried out to assess the validity and the accuracy of this improved material description.

A simple model for dislocation behavior, strain and strain rate hardening evolution in deforming aluminum alloys

In this work, modeling of the stress–strain behavior is carried out using a simple dislocation model. This model uses three variables to characterize the dislocation population: The average forest and mobile dislocation densities, ρf and ρm, and the average dislocation mean free path L. However, it is shown that within reasonable assumptions, only two of these variables are independent. The mathematical form derived from this dislocation-based model was applied to experimental stress–strain data determined at room temperature for pure aluminum, 3003-O, 2008-T4, 6022-T4, 5182-O and 5032-T4 aluminum alloy sheets. The evolution of the state variables was calculated for these materials from a single stress–strain curve. The average dislocation mean free paths at a strain of 0.5 were compared with TEM observations of dislocation cell sizes or inter-dislocation spacing for specimens deformed equal biaxially with the hydraulic bulge test. A very good agreement was obtained between predictions and experiments.

Blank shape design for a planar anisotropic sheet based on ideal forming design theory and FEM analysis

Abstract A sequential design procedure to optimize sheet forming processes was developed utilizing ideal forming design theory, FEM analysis and experimental trials. For demonstration purposes, this procedure was used to design a blank shape for a highly anisotropic aluminum alloy sheet (2090-T3) that results in a deep-drawn, circular cup with minimal earing. All blank shape design methods require a certain number of iterations. However, the sequential procedure can be more effective than the other iterative methods based on FEM analysis in conjunction with experimental trials or on experimental trials alone. For this design demonstration, the anisotropic constitutive behavior of the 2090-T3 sheet was expressed using plastic potentials previously proposed by Barlat et al . The implementation of the anisotropic strain-rate potential in the ideal forming design code is also briefly summarized.

Characterization and modeling of the mechanical behavior and formability of a 2008-T4 sheet sample

Abstract A 2008-T4 sheet sample has been characterized and its mechanical behavior and formability have been modeled. Uniaxial tensile and equal biaxial tensile stress-strain data, compressive yield strengths, crystallographic texture, earing and the forming limit curve were experimentally determined. Bulge test specimen shape and thickness profiles were also measured after various amounts of biaxial strain. A recently developed phenomenological constitutive model of anisotropic mechanical behavior was used to predict the directionality of strength, plastic strain ratio ( R ) and shear strain ratio (Г) values. In addition, this model was used to predict the forming limit curve for this sample. Predictions made with the recent model generally compare favorably with experimental results and with predictions made using the Taylor/Bishop and Hill theory. According to the data obtained in hydraulic bulge testing, the 2008-T4 exhibited apparent isotropic behavior. However, in cup drawing—another axisymmetric deformation mode—this material exhibited anisotropic behavior, as indicated by the formation of ears and troughs.

Experimental analysis of aluminum yield surface for binary AlMg alloy sheet samples

Abstract In this work, the yield surfaces of binary aluminum-magnesium alloy sheet samples were measured using biaxial compression tests. Sheet samples of a given material were stacked and bonded together with epoxy and cubic compression specimens were machined out of the laminate. The yielding behavior was assumed to be independent of the hydrostatic pressure. In the analysis of the biaxial compression tests, the effects of friction and of the elasticity of the die were accounted for. These effects were studied with the aid of finite element method (FEM) simulations of the test which proved to be useful in avoiding systematic errors. The yield surfaces of three binary alloy sheet samples containing 5 wt% Mg but with different crystallographic textures were analyzed. The different textures resulted from processing under different thermomechanical conditions. The experimental yield surfaces were compared to predictions made with the Taylor-Bishop and Hill (TBH) model and with a phenomenological yield function. The experimental and polycrystal yield surfaces were found to be in fair agreement. The yield function was found to be a suitable description of the plastic behavio for only two of the materials studied.

Characterizations of Aluminum Alloy Sheet Materials Numisheet 2005

This report reproduces the contents of a document provided in the Numisheet 2005 Benchmark Study for the characterization of aluminum alloys.

Yield and Strain Rate Potentials for Aluminum Alloy Sheet Forming Design

In this paper, potentials that analytically describe the plastic behavior of orthotropic metals are reviewed. These potentials, yield functions or strain rate potentials were expressed in six-dimensional stress or strain rate spaces, respectively. Some of the recently developed potentials that are consistent with polycrystal plasticity models are briefly discussed and applied to computational analysis and design of sheet metal forming processes.